Department of Mathematics, University of Neyshabur
Abstract
We define a new type of spectrum, called δ-approximate spectrum, of an element a in a complex unital Banach algebra A and show that the δ-approximate spectrum σ_δ (a) of a is compact. The relation between the δ-approximate spectrum and the usual spectrum is investigated. Also an analogue of the classical Gleason-Kahane-Zelazko theorem is established: For each ε>0, there is δ>0 such that if ϕ is a linear functional with ϕ(a)∈σ_δ (a) for all a∈A, then ϕ is ε-almost multiplicative. Finally, we use these ideas to provide a sufficient condition for a δ-almost multiplicative functional to be multiplicative.
Anjidani, E. (2015). Almost multiplicative linear functionals and approximate spectrum. Bulletin of the Iranian Mathematical Society, 41(1), 177–187.
MLA
Anjidani, E. "Almost multiplicative linear functionals and approximate spectrum", Bulletin of the Iranian Mathematical Society, 41, 1, 2015, 177–187.
HARVARD
Anjidani, E. (2015). 'Almost multiplicative linear functionals and approximate spectrum', Bulletin of the Iranian Mathematical Society, 41(1), pp. 177–187.
CHICAGO
Anjidani, E., "Almost multiplicative linear functionals and approximate spectrum." Bulletin of the Iranian Mathematical Society, 41 1 (2015): 177–187,
VANCOUVER
Anjidani E. Almost multiplicative linear functionals and approximate spectrum. BIMS. 2015;41(1):177–187.
